the development of poiseuille flow of a pseudoplastic fluid
the development of poiseuille flow of a pseudoplastic fluid the development of poiseuille flow of a pseudoplastic fluid
108 M.A.M. Al Khatib Examples of the eigenvalues are given in Tables 2, 3, and 4 for the same values of k used to draw the velocity profiles in Figures 2, 3, and 4. Table 2. The Leading Eigenvalue α for the Case k =2and n → 0. n α 1.000 2.106196 + i1.125364 0.900 2.063433 + i1.116431 0.800 2.014212 + i1.106579 0.700 1.956469 + i1.095871 0.600 1.886985 + i1.084694 0.500 1.800307 + i1.074300 0.400 1.685923 + i1.068200 0.300 1.519094 + i1.074583 0.200 1.225893 + i1.094100 0.150 0.975289 + i1.068689 0.100 0.626237 + i 0.902539 0.050 0.218521 + i 0.380135 0.040 0.132731 + i 0.230975 0.030 0.059276 + i 0.109136 0.025 0.022121 + i 0.048524 0.024 0.014812 + i 0.036458 0.023 0.007509 + i 0.025245 0.022 0.000353 + i 0.014025 Table 3. The Leading Eigenvalue α for the Case k =10and n → 0. n α 1.00 2.106196 + i1.125364 0.90 2.035593 + i1.128023 0.80 1.955879 + i1.135971 0.70 1.863159 + i1.152236 0.60 1.748825 + i1.180960 0.50 1.592574 + i1.223862 0.40 1.353831 + i1.260822 0.30 0.992884 + i1.205290 0.20 0.544458 + i 0.881442 0.15 0.309815 + i 0.565653 0.12 0.155244 + i 0.392127 0.11 0.105398 + i 0.332444 0.10 0.054936 + i 0.272450 0.09 0.004784 + i 0.218245 The Arabian Journal for Science and Engineering, Volume 31, Number 1A. January 2006
Table 4. The Leading Eigenvalue α for the Case k =0.5 and n → 0. n α 1.00 2.106196 + i1.125364 0.90 2.098909 + i1.122195 0.80 2.091326 + i1.118841 0.70 2.083419 + i1.115280 0.60 2.075158 + i1.111489 0.50 2.066506 + i1.107441 0.40 2.057417 + i1.103102 0.30 2.048824 + i1.098916 0.20 2.037720 + i1.093385 0.10 2.026973 + i1.087899 0.00 2.015508 + i1.081899 M.A.M. Al Khatib From Tables 2, 3, and 4 and the corresponding graph given in Figure 5, it appears that when k = 2 and k = 10, Re(α) → 0 as the power law index, n → 0.0220 and 0.0892 respectively. This implies that, when k =2 and k = 10, the parallel flow is unstable for 0
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- Page 3 and 4: 3. EQUATIONS OF MOTION M.A.M. Al Kh
- Page 5 and 6: velocity 0.6 0.5 0.4 0.3 0.2 0.1 0
- Page 7: M.A.M. Al Khatib respectively. Exam
Table 4. The Leading Eigenvalue α for <strong>the</strong> Case k =0.5 and n → 0.<br />
n α<br />
1.00 2.106196 + i1.125364<br />
0.90 2.098909 + i1.122195<br />
0.80 2.091326 + i1.118841<br />
0.70 2.083419 + i1.115280<br />
0.60 2.075158 + i1.111489<br />
0.50 2.066506 + i1.107441<br />
0.40 2.057417 + i1.103102<br />
0.30 2.048824 + i1.098916<br />
0.20 2.037720 + i1.093385<br />
0.10 2.026973 + i1.087899<br />
0.00 2.015508 + i1.081899<br />
M.A.M. Al Khatib<br />
From Tables 2, 3, and 4 and <strong>the</strong> corresponding graph given in Figure 5, it appears that when k = 2 and<br />
k = 10, Re(α) → 0 as <strong>the</strong> power law index, n → 0.0220 and 0.0892 respectively. This implies that, when k =2<br />
and k = 10, <strong>the</strong> parallel <strong>flow</strong> is unstable for 0
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